Prepare an ice bath by filling a large bowl with ice cubes and some water. Place another, smaller bowl on top of the water, and place a strainer inside. Keep this close by while you make the ice cream base.
Whisk the yolks and sugar until pale lemon-yellow colored: If you haven't already done so, separate the yolks from the eggs. Combine the yolks and the sugar in a medium mixing bowl. Whisk until combined — at first the mixture will be very thick and dark yellow, then it will smooth out and lighten to a pale lemon-yellow color.
Warm the milk on the stovetop: Pour the milk into a medium saucepan and place over medium heat. Add the vanilla bean (pod and seeds) or vanilla extract. Bring the milk to a simmer, then remove from heat.
Temper the egg-sugar mixture with 1 cup of hot milk: Scoop out about 1 cup of hot milk (no need to be exact). Slowly pour it into the egg-sugar mixture while whisking. This warms the eggs and prevents them from curdling in the next step.
Pour the tempered egg-sugar mixture into the milk: Slowly pour the tempered egg-sugar mixture into the saucepan with the remaining milk.
Cook the ice cream base until thickened: Return the saucepan to the stove and place over low heat. Stir the mixture slowly, but constantly, scraping the bottom and sides of the pot. Keep cooking until the base has thickened enough to coat the back of the spatula and registers 170°F with an instant-read thermometer.
Strain the ice cream base into the bowl of the ice water bath. Straining will remove the vanilla pod and any bits of egg that may have accidentally curdled.
Stir the heavy cream into the ice cream base.
Chill completely: Leave the ice cream base over the ice water bath, stirring occasionally, until it's completely chilled. This will take about 20 minutes. Alternatively, cover the bowl with the base and chill in the fridge for 3 hours or overnight.
Churn the ice cream base: Transfer the ice cream base to the bowl of your ice cream machine. Churn until the base has thickened to a consistency somewhere between a very thick milkshake and soft-serve ice cream. In most ice cream makers, this takes about 20 minutes — check the instructions for your particular machine.
Freeze the ice cream until solid: Transfer the thickened ice cream to a freezer container. Press a piece of wax paper against the surface of the ice cream to prevent ice crystals from forming and freeze until solid, at least 4 hours. The ice cream will keep in the freezer for about 2 weeks before becoming icy.